Duality for local fields and sheaves on the category of fields

Abstract

Duality for complete discrete valuation fields with perfect residue field with coefficients in (possibly p-torsion) finite flat group schemes was obtained by Begueri, Bester and Kato. In this paper, we give another formulation and proof of this result. We use the category of fields and a Grothendieck topology on it. This simplifies the formulation and proof and reduces the duality to classical results on Galois cohomology. A key point is that the resulting site correctly captures extension groups between algebraic groups.

Accepted for publication in the Kyoto Journal of Mathematics. 63 pages

References in corpus (2)

• Grothendieck's pairing on Neron component groups: Galois descent from the semistable case
• A refinement of the local class field theory of Serre and Hazewinkel

Cited by in corpus (6)

• Duality for cohomology of curves with coefficients in abelian varieties
• Arithmetic duality for two-dimensional local rings with perfect residue field
• On $\mu$-invariants and isogenies for abelian varieties over function fields
• Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings
• An improvement of the duality formalism of the rational etale site
• Duality theories for p-primary etale cohomology III